Question

The Associative Property
a + (b+c) = (a+___) + c
7+ (5-7)=7+5+(-7)
Use the Commutative Property:
7+1 (____) + 5
Use the Associative Property:
[17 + (-7)] + 5=___

Answers

Answered by GPT-4o mini
Let's go through each of your statements step by step.

1. For the Associative Property:
\( a + (b+c) = (a+b) + c \)

If we let \( a = 7 \), \( b = 5 \), and \( c = -7 \), we need to fill in the blank in the equation \( 7 + (5 + (-7)) = (7 + \_\_) + (-7) \).

According to the Associative Property:
\( 7 + (5 + (-7)) = (7 + 5) + (-7) \)
So, \( 7 + \_\_ = 7 + 5 \) means \( \_\_ = 5 \).

2. Using the Commutative Property:
The Commutative Property states that:
\( a + b = b + a \)

For \( 7 + 1 \), we can express it as \( 1 + 7 \), and this means:
\( 7 + 1 = \_\_ + 5 \)

To find \( \_\_ \), we can use \( 1 + 7 = 8 \) and therefore:
\( 8 = \_\_ + 5 \)
Thus, \( \_\_ = 8 - 5 = 3 \).

3. For the last part using the Associative Property:
We have:
\([17 + (-7)] + 5\)

Using the Associative Property:
We can rearrange it like this:
\([17 + (-7)] + 5 = 17 + [(-7) + 5]\).

We know that \((-7) + 5 = -2\), so it simplifies to:
\(17 + (-2) = 15\).

In conclusion:
1. The first blank is **5**.
2. The second blank is **3**.
3. The final answer is **15**.
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